Len Wiseman and Kate Beckinsale met on the set of “Underworld” in 2003. The encounter reportedly broke up two relationships. Photo: Getty Images

She was literally his dream girl, conjured in his artwork.

When director Len Wiseman sat down to sketch the main character in his 2003 vampires-versus-werewolves film “Underworld,” he drew the spitting image of Kate Beckinsale, the Brit actress whom he’d never met but would go on to play the part and eventually become his wife.

“The script called for a gorgeous vampire goddess, and the chances are that my idea of a goddess will look pretty close to the kind of person I fall in love with,” Wiseman once told the London Evening Standard.

The couple has made two films together. On Friday, their third, “Total Recall,” opens. The thriller is a remake of the 1990 Arnold Schwarzenegger original in which a blue-collar worker (Colin Farrell) agrees to have fake memories implanted in his brain. When the process goes wrong, he finds himself on the run, and the line between reality and fantasy begins to bleed.

Beckinsale, 39, plays Farrell’s wife, who (it’s no spoiler to say) turns on him and ends up trying to kill him.

Since they got together in 2003, Beckinsale and Wiseman have been tabloid fixtures here and especially in her native UK, filling the pages alternately with rumors of splits and her gushing, TMI-ish nuggets about their personal life.

Here’s the annotated version of the latter: They enjoy webcam sex. He likes her in leather. He also enjoyed it when she filled out for a role and had “a bigger bottom and boobs.” To make up for the lack of sleeping around in her life, Beckinsale tries having “sex many, many, many times with one person.”

The pair met working on “Underworld,” which proved to be a breakout hit for them both. Previously, the California-born Wiseman, 39, had been a commercial and music-video director.

The only problem was, both were in long-term relationships. Beckinsale had been together with actor Michael Sheen (of “Frost/Nixon”) for eight years, and the two had a daughter, Lily, in 1999. Wiseman was married to Dana Wiseman, a schoolteacher.

Both the actress and the director have denied that they got together while the movie was shooting, but in interviews, Dana has claimed otherwise.

Whenever the romance started, it quickly became serious. They married in 2004 at the Hotel Bel-Air and then honeymooned in Mexico, where Beckinsale donned a white bikini with the name “Mrs. Wiseman” stitched across her butt.

“I’ve never come across anybody as steady and calm as Len is,” she told Self magazine. “I’m the one who’s a bit more volatile, spontaneous, mercurial. And Len is like the glue. And he’s incredibly handsome, which really helps.”

She has also said that Wiseman made her feel sexy for the first time in her life and that she valued him for asking her to marry him — something, she pointed out, that did not happen in her time with Sheen.

Something else that also did not happen until Beckinsale met Wiseman was her transformation to action star. Before “Underworld” gave her the chance to put on tight spandex, grab a gun and wire-fight in slo-mo, she’d been known mostly for restrained costume dramas, including “Emma” and “The Golden Bowl.”

But outside of the “Underworld” franchise and projects directed by her husband, Beckinsale has sometimes stumbled. “Whiteout,” from 2009, gave her a headlining role but bombed. The same year, “Nothing But the Truth” went straight to DVD. That year’s “Everybody’s Fine,” a family drama with Robert De Niro, was mostly panned.

Following 2009’s troubles, she took a three-year hiatus from movies, returning earlier this year in “Contraband.”

She has said she wanted to focus on her family. Perhaps not coincidentally, separation rumors have followed her and Wiseman for years. In 2006, she reportedly moved out and was looking for new digs with her daughter.

The couple apparently reconciled, although there have been rumors of fighting on set. During a recent appearance on “The Tonight Show,” Beckinsale joked about keeping her arguments with Wiseman private while filming. Instead of yelling, they now text each other. “You’d be amazed how fast you can type ‘douchebag,’ ” she said.

Careful there. A few harsh words, and the next thing you know, Wiseman could be taking up with Kristen Stewart. We hear she likes directors.